Related papers: Open aspherical manifolds not covered by the Eucli…

We present an explicit construction of closed oriented aspherical smooth 4-manifolds with $\chi = \sigma = n$ for every positive integer $n$. This proves a conjecture of Edmonds by providing a closed oriented aspherical 4-manifold with…

We obtain some restrictions on the topology of infinite volume hyperbolic manifolds. In particular, for any n and any closed negatively curved manifold M of dimension greater than 2, only finitely many hyperbolic n-manifolds are total…

We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod $p$ acyclic in the finite…

In this paper, an n-dimensional complete open manifold with nonnegative Ricci curvature and collapsing volume has been investigated. If its radial sectional curvature bounded from below, it shows that such a manifold is of finite…

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. We show that a complete noncompact manifold with asymptoticaly nonnegative Ricci curvature and sectional…

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…

Let $X$ be an elliptic curve and $\mathbb{P}$ the Riemann sphere. Since $X$ is compact, it is a deep theorem of Douady that the set $\mathcal{O}(X,\mathbb{P})$ consisting of holomorphic maps $X\to \mathbb{P}$ admits a complex structure. If…

Let O be a compact orientable 3-orbifold with non-empty singular locus and a finite volume hyperbolic structure. (Equivalently, O is the quotient of hyperbolic 3-space by a lattice in PSL(2,C) with torsion.) Then we prove that O has a tower…

Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of such manifolds. In…

In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the…

We show that, if a closed, connected, and oriented Riemannian $n$-manifold $N$ admits a non-constant quasiregular mapping from the Euclidean $n$-space $\mathbb R^n$, then the de Rham cohomology algebra $H_{\mathrm{dR}}^*(N)$ of $N$ embeds…

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…

We present a family of examples of two dimensional, hyperbolic complex manifolds whose envelopes of holomorphy are not hyperbolic.

We prove that a class of asymptotically nonnegatively curved manifolds (in the sense of Abresch) satisfying some uniform Euclidean type volume growth conditions contains only finitely many homeomorphism types.

Locally standard $T$-pseudomanifolds were introduced by the authors in a previous work. They are topological stratified pseudomanifolds equipped with torus actions. Their equivariant homeomorphism types are classified by characteristic data…

The main result in this paper is that the space of all smooth links in Euclidean 3-space isotopic to the trivial link of n components has the same homotopy type as its finite-dimensional subspace consisting of configurations of n unlinked…

A closed connected hyperbolic $n$-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic $(n+1)$-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many…

In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes,…

We consider non-orientable hyperbolic 3-manifolds of finite volume $M^3$. When $M^3$ has an ideal triangulation $\Delta$, we compute the deformation space of the pair $(M^3, \Delta)$ (its Neumann Zagier parameter space). We also determine…

We analyse properties of hypertoric manifolds of infinite topological type, including their topology and complex structures. We show that our manifolds have the homotopy type of an infinite union of compact toric varieties. We also discuss…